USA has always been called "America". Europe the continent has been Europe the continent far longer than the EU has existed. Both are incorrect, and thankfully "The Americas" has caught on to fix one of these wrong labels. Besides, the continent has always been called North America, not America. There is no other label of Europe the continent than "Europe", so it's a flat out wrong label of the EU at best, and at worst it's offensive to those not living in the Alliance.
I have never understood calling Europe a continent. The division strikes me as political rather than geographic. And no, I can't be convinced otherwise.
let's go with a practical definition like "within all living memory" which most people, I'm sure, presumed from context. very few people need their conversations to include the mental state of those dead for 200+ years simply to achieve some stringent ideal of correctness.